Exam Body

Year

Subject

Paper Type

neco 2024 further_mathematics | Objective

Prepare for your exams with neco questions? Reviewing past/model questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2024 further_mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1 View Details

Find the complex number \(z\) such that \(\displaystyle\frac{z-2i}{\,z+2i\,}\) is a real number, \(|z|=5\) and the argument of \(z\) lies between \(0\) and \(\pi\) radians. Determine \(z\) in the form \(a+bi\).

A. -5i

Correct B. 5i

C. 3i

D. 2i

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 2 View Details

Let \(A=\{1,2,3,4\}\) and \(B=\{2,4,6,8\}\). Define the relation \(R=\{(x,y)\in A\times B\mid x\text{ divides }y\}\). List all ordered pairs in \(R\) and state whether \(R\) is a function from \(A\) to \(B\).

A. R = {(1,2),(1,4),(1,6),(1,8),(2,2),(2,4),(2,6),(2,8),(3,6),(4,4),(4,8)}; is a function

B. R = {(1,2),(1,4),(1,6),(1,8),(2,2),(2,4),(2,6),(2,8),(4,4),(4,8)}; not a function

Correct C. R = {(1,2),(1,4),(1,6),(1,8),(2,2),(2,4),(2,6),(2,8),(3,6),(4,4),(4,8)}; not a function

D. R = {(1,2),(1,4),(1,6),(1,8),(2,2),(2,4),(2,6),(2,8),(3,6),(4,4)}; not a function

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 3 View Details

Evaluate the integral \(\displaystyle\int \frac{2x^{2}+3x+5}{(x+1)(x^{2}+1)}\,dx\).

A. \ln|x+1| + 3\arctan x + C

Correct B. 2\ln|x+1| + 3\arctan x + C

C. 2\ln|x-1| + 3\arctan x + C

D. 2\ln|x+1| + \arctan x + C

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 4 View Details

Solve for \(\theta\) in the interval \(0^{\circ}\le \theta <360^{\circ}\) the equation \(\sin 2\theta = \sqrt{3}\cos\theta\).

A. 30°, 90°, 150°, 270°

B. 45°, 90°, 135°, 270°

Correct C. 60°, 90°, 120°, 270°

D. 60°, 150°, 210°, 300°

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 5 View Details

Simplify \(\log_{2} 8^{\log_{3} 27}\) and give the exact integer value.

A. 12

B. 6

Correct C. 9

D. 27

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 6 View Details

The matrix \(A = \begin{pmatrix}2 & k\\ k & 5\end{pmatrix}\) has determinant \(7\). Find the value of \(k^{2}\) and then compute the trace of \(A^{2}\).

A. 45

B. 30

Correct C. 35

D. 40

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 7 View Details

Simplify the expression \(\frac{2^{5}\cdot\sqrt{8}}{4^{3}}\) and write the result as a power of \(2\).

A. 2^{1\/3}

Correct B. 2^{1/2}

C. 2^{3\/2}

D. 2^{2\/1}

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 8 View Details

In the plane, vectors \(\mathbf{a}\) and \(\mathbf{b}\) satisfy \(|\mathbf{a}| = 5\) and \(|\mathbf{b}| = 3\). If the vector \(\mathbf{a} + 2\mathbf{b}\) is perpendicular to \(2\mathbf{a} - \mathbf{b}\), find the dot product \(\mathbf{a}\cdot\mathbf{b}\).

A. -32/9

Correct B. -32/3

C. -16/3

D. 32/3

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 9 View Details

The circle \(x^{2} + y^{2} - 6x + 8y + 9 = 0\) has centre \(C\) and radius \(r\). A line passes through the point \(P(10,0)\) and is tangent to the circle. Determine the possible slopes of the tangent line.

A. 0 and -56/33

B. 0 and 55/33

Correct C. 0 and 56/33

D. 0 and 56/31

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 10 View Details

Let \(f(x) = 2x + 3\) and \(g(x) = x^{2}\). Find the value of the composition \((f\circ g)(-2)\).

A. 9

Correct B. 11

C. 7

D. 1

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 11 View Details

In a right‑angled triangle, the acute angle \(\theta\) satisfies \(\sin\theta = \frac{3}{5}\) and another acute angle \(\phi\) satisfies \(\tan\phi = 2\). Find the exact value of \(\sin(\theta+\phi)\).

A. \frac{9\sqrt{5}}{25}

Correct B. \frac{11\sqrt{5}}{25}

C. \frac{11\sqrt{5}}{20}

D. \frac{11\sqrt{5}}{30}

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 12 View Details

The curve is defined by \(y^{2}=x^{3}+6x^{2}+k\) and passes through the point \((2,5)\). (a) Determine the value of \(k\). (b) Find \(\displaystyle\frac{dy}{dx}\) at that point.

A. -18/5

Correct B. 18/5

C. 36/5

D. 9/5

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 13 View Details

A particle moves along a straight line with position function \(s(t)=t^{3}-6t^{2}+9t\) metres, where \(t\) is in seconds. In the interval \(0\le t\le 6\), at what time does the particle attain its maximum speed? Give your answer to the nearest second.

A. 3

B. 4

Correct C. 6

D. 5

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 14 View Details

A uniform beam \(AB\) 6\,m long is hinged at \(A\) to a vertical wall. The beam makes an angle of \(30^{\circ}\) with the horizontal. A cable \(BD\) is attached to the free end \(B\) and to a point \(D\) on the wall 4\,m directly above \(A\). A vertical downward load of 800\,N is applied at a point 2\,m from \(A\) along the beam. Determine the tension in the cable (in newtons), giving your answer in exact surd form.

Correct A. (400\sqrt{7})/3

B. (200\\sqrt{7})\/3

C. (400\\sqrt{5})\/3

D. (400\\sqrt{7})\/2

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 15 View Details

A committee of five members is to be chosen from eight teachers and six students. The committee must contain at least two teachers and at most three students. How many different committees can be formed?

A. 1920

Correct B. 1876

C. 2002

D. 1760

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 16 View Details

A factory produces widgets of type X and Y. 60% of the widgets are type X and 40% are type Y. An inspection test correctly identifies a type X widget with probability (0.90) and correctly identifies a type Y widget with probability (0.80). Each widget is inspected twice independently. A widget is reported as type X on both inspections. The widget will be sold only if it is reported as type X on both inspections. The profit earned on selling a type X widget is ₦500 and on selling a type Y widget is ₦300. What is the expected profit per widget produced (in Naira)?

A. 225.5

B. 300.0

Correct C. 247.8

D. 260.0

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 17 View Details

Let \(T:\mathbb{R}^2\to\mathbb{R}^2\) be a linear transformation represented by the matrix \(\begin{pmatrix}a&b\\c&d\end{pmatrix}\). It is known that \(T(1,2) = (4,1)\) and \(T(3,-1) = (k,6)\). Moreover, the determinant of the matrix is \(2\) and \(T(2,1) = (5,-1)\). Find the value of \(k\) and then determine the image of the vector \((2,5)\) under \(T\). Express your answer as \(k = \dots\) and \(T(2,5) = (\dots,\dots)\).

A. k = 5; T(2,5) = (8, 11\/4)

Correct B. k = 5; T(2,5) = (9, 11/4)

C. k = 5; T(2,5) = (9, 10\/4)

D. k = 4; T(2,5) = (9, 11\/4)

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 18 View Details

In triangle \(ABC\), side \(AB = 8\) cm, side \(AC = 6\) cm and \(\angle BAC = 60^{\circ}\). Let \(D\) be the foot of the altitude from \(A\) to side \(BC\). Find the length of segment \(BD\). Give your answer in simplest surd form.

A. 20\\sqrt{13}\/7

Correct B. 20\sqrt{13}/13

C. 16\\sqrt{13}\/13

D. 20\\sqrt{7}\/13

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 19 View Details

A 5 kg block rests on a plane inclined at \(30^{\circ}\) to the horizontal. The coefficient of kinetic friction between the block and the plane is \(\mu_{k}=0.20\). The block is attached by a light inextensible string over a frictionless pulley to a 3 kg hanging mass. Determine (i) the magnitude of the acceleration of the system and (ii) the tension in the string. State the direction of motion of each mass.

A. a = 0.30 m\/s^2 (block up the incline, hanging mass down); T ≈ 25.0 N

B. a = 0.45 m\/s^2 (block down the incline, hanging mass up); T ≈ 28.1 N

C. a = 0.60 m\/s^2 (block down the incline, hanging mass up); T ≈ 31.5 N

Correct D. a = 0.45 m/s^2 (block up the incline, hanging mass down); T ≈ 28.1 N

Correct Answer: D

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 20 View Details

Evaluate the integrals \(I = \int_{0}^{1} \frac{x^{3}}{\sqrt{1 - x^{2}}}\,dx\) and \(J = \int_{0}^{1} \frac{x}{\sqrt{1 - x^{2}}}\,dx\), then find the value of the ratio \(\frac{I}{J}\).

Correct A. 4/3

B. 5/3

C. 2/3

D. 3/4

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 21 View Details

A quiz team is to be formed from 9 students. The team must consist of a captain, a vice‑captain, a question‑writer and an answer‑writer (all distinct), and one additional member with no special role. Two particular students, A and B, refuse to be on the same team. How many possible arrangements of the five positions are there?

Correct A. 10920

B. 15120

C. 10800

D. 11520

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 22 View Details

A complex number \(z\) satisfies \(\frac{z+1}{z-1}=i\sqrt{3}\). Find the value of \(z^{2}+\frac{1}{z^{2}}\).

A. \frac{-17+15 i\sqrt{3}}{8}

B. \frac{-17-5 i\sqrt{3}}{8}

C. \frac{17-15 i\sqrt{3}}{8}

Correct D. \frac{-17-15 i\sqrt{3}}{8}

Correct Answer: D

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 23 View Details

Simplify \(\frac{2^{4}\cdot5^{2}}{10^{3}}\) and give the answer as a fraction in lowest terms.

A. 2/3

B. 1/5

C. 4/5

Correct D. 2/5

Correct Answer: D

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 24 View Details

Seven distinct novels are to be placed on a single shelf. Novel C must be placed at either end of the shelf, and novels A and B must not be adjacent. How many possible arrangements satisfy these conditions?

A. 1440

B. 720

C. 480

Correct D. 960

Correct Answer: D

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 25 View Details

Three vectors \(\mathbf{u}, \mathbf{v}, \mathbf{w}\) in a plane satisfy \(\mathbf{u}+\mathbf{v}+\mathbf{w}=\mathbf{0}\). The magnitudes are \(|\mathbf{u}|=5\) and \(|\mathbf{v}|=7\), and the angle between \(\mathbf{u}\) and \(\mathbf{v}\) is \(120^{\circ}\). Find (i) the magnitude of \(\mathbf{w}\) and (ii) the angle between \(\mathbf{w}\) and \(\mathbf{u}\) (to the nearest degree).

A. |\\mathbf{w}| = \\sqrt{41}, angle \\approx 110^{\\circ}

Correct B. |\mathbf{w}| = \sqrt{39}, angle \approx 104^{\circ}

C. |\\mathbf{w}| = 12, angle \\approx 90^{\\circ}

D. |\\mathbf{w}| = \\sqrt{35}, angle \\approx 95^{\\circ}

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Master the Exam!

You've seen a preview, but there are thousands more questions plus AI tutor to break down complex solutions.

Unlock Full Access Available for Android & Windows

Help others prepare! Share this practice hub:

Chat with Support